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Lately there have been several threads about changing the differential on Ron's and other M Coupes. During casual conversation at the track, it was suggested that I think about doing the same to my 99 2.8 Z3 Coupe.

What I would like to know is what does one gain or lose by such a modification? I assume that it keeps the engine in the greatest
torque producing area of the performance curve. But I will be the first to admit that I really don't know.

Think about a multi-gear bicycle....smaller gear in front, larger in back makes it really easy to pedal quickly, but it takes a lot more RPM to make speed. Higher gear ratio makes it easier to deliver higher torque to the wheels making the torque requirements on the "engine" lower.

Increasing the ratio of the final drive results in that same relationship: smaller front gear (pinion) to rear gear (ring) ratio. The result is a final drive system that is easier for the engine to turn faster, but that also results in a more rapid climb in RPMs.

It's all a balancing act... too high a ratio and you'll peak on RPMs too quickly and not be able to reach enough speed in each gear, too low a ratio and your final drive takes longer to get up to speed because it's "harder to turn" and is requires more torque from the engine.

Having a 3.46 in my '01 M Coupe for a month now I agree with Ron's sentiments that the 3.46 is a better ratio for the S54 engine. I don't know if the S52 would be the same because that engine has a lower redline and perhaps a less flat torque curve. It may be that S52 M Coupe/Roadsters are already optimally geared.

The torque delivered at the rear wheel is actually the engine torque multiplied by the gears in the transmission. If you're in first gear with a 4.21 1st gear and a 3.15 final drive gear (differential), you end up with the engine torque x 4.21 x 3.15. What this means is that the "shorter" the differential (which means a higher number and a higher multiplier), you deliver more torque to the rear wheels. Torque is the force that's going to twist the wheel, and, in turn, make your car go. The more torque you have, the faster your acceleration. This is why a shorter differential will make your car goes faster.

The downside is that you're using up your engine's speed faster. Since more turns are going into every one turn of the wheel, when you're redlining the engine, your wheel is turning slower than it was before. This means more shifts to accelerate the same amount, a higher cruising speed, and a lower maximum speed.

Changing differentials is simple physics: a 10% shorter differential (such as a 3.15->3.46) means that your torque is 10% greater, so acceleration should be 10% faster (in theory, at least), cruising rpm at x mph will be 10% higher, and your maximum speed in 5th gear will be 10% lower.